I am unable to use Logitech Performance MX mouse back and forward buttons in Windows virtual machine. They do not work in any browser or Windows File Explorer, however they work fine on the Mac side.
Default shortcut key mapping cannot be applied in Windows virtual machine.
Download and open Logitech Options on the Mac.
Choose Forward button > scroll down until you find Keystroke assignment option.
Click it, then hit right arrow on your keyboard to create a shortcut.
Do likewise with Back button and left arrow.
Click on Parallels Desktop icon on Mac menu bar > choose Preferences.
Go to Shortcuts > find your Windows virtual machine in the virtual machines list > click '+' to add the shortcut > make sure your Back and Forward button shortcuts match the ones on the screenshots below: